CN107618678B - Attitude control information joint estimation method under satellite attitude angle deviation - Google Patents
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Abstract
An attitude control information joint estimation method under satellite attitude angle deviation relates to the technical field of satellite attitude determination and control. The method is based on measurement information of a satellite-borne sensor and an execution mechanism, under the small-angle deviation of the attitude, joint accurate estimation of variables such as a satellite attitude error quaternion, a satellite attitude error angular velocity, a reaction flywheel angular momentum, a reaction flywheel friction torque, an external interference torque, a fiber-optic gyroscope constant drift and the like is achieved in a cyclic iteration mode by utilizing satellite attitude dynamics, kinematics and a reaction flywheel dynamics model, and accurate attitude control information is provided for high-precision satellite attitude control. The method is realized only by a software algorithm, and is simple and easy to operate.
Description
Technical Field
The invention relates to the technical field of satellite attitude determination and control, in particular to an attitude control information joint estimation method under small-angle deviation of satellite attitude.
Background
The high-precision control of the satellite attitude depends on a sensor and an actuating mechanism, an attitude determination algorithm and an attitude control algorithm. In the case of hardware configuration determination, the control performance is improved mainly by software. The attitude determination algorithm mainly calculates attitude control information required by the satellite attitude control algorithm, the influence of the amount and the accuracy of the information on the overall control performance of the satellite attitude is large, particularly after the satellite attitude completes large-angle maneuvering, the convergence precision of the satellite attitude is influenced in the process of approaching the target attitude, and the pointing direction and the stability of the satellite attitude are finally influenced.
Generally, a satellite attitude control algorithm needs an accurate attitude error quaternion and an attitude error angular velocity to calculate a satellite attitude control moment, but the actual control moment acting on the satellite attitude is influenced due to factors such as friction moment of a reaction flywheel equiangular momentum executing mechanism, interference moment of a space environment, fiber optic gyroscope drift and the like. If the quaternion of the attitude error and the angular velocity of the attitude error can be accurately estimated, the angular momentum of a reaction flywheel, the friction moment of the reaction flywheel, the external disturbance moment, the constant drift of the fiber-optic gyroscope and the like are accurately estimated, and compensation is performed in an attitude control algorithm, so that the overall performance of the attitude control of the satellite is greatly improved.
Disclosure of Invention
The invention provides a combined estimation method of attitude control information under small angle deviation of satellite attitude, aiming at solving the problem of low control precision caused by difficult accurate estimation of the attitude control information under small angle deviation of the attitude in the maneuvering process of satellite attitude.
The attitude control information joint estimation method under the satellite attitude angle deviation specifically comprises the following steps:
respectively acquiring current measurement values of a star sensor, a fiber-optic gyroscope, a reaction flywheel and a GPS through a satellite-borne central machine to obtain a satellite attitude measurement quaternion, a satellite attitude measurement angular velocity, an angular momentum of the reaction flywheel and GPS time information at the current moment, and respectively performing deviation calculation on a given expected attitude quaternion and an expected attitude angular velocity with the satellite attitude measurement quaternion and the satellite attitude measurement angular velocity at the current moment to obtain a satellite attitude error quaternion and a satellite attitude error angular velocity at the current moment; simultaneously, recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment;
recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment based on the step one, and respectively calculating a satellite attitude error quaternion derivative, a satellite attitude error angular velocity derivative and a reaction flywheel angular momentum derivative according to a satellite attitude dynamics and kinematics equation and a reaction flywheel dynamics model; setting the derivative of the friction torque of the reaction flywheel as zero, the derivative of the external disturbance torque as zero, and the derivative of the constant drift of the fiber-optic gyroscope as zero;
step three, taking the quaternion estimation value of the satellite attitude error, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of the reaction flywheel, the friction torque estimation value of the reaction flywheel, the external disturbance torque estimation value and the constant offset estimation value of the fiber-optic gyroscope recorded in the step one as initial values,
taking a preset control period as an integral duration, and obtaining a one-step predicted value of the satellite attitude error quaternion, a one-step predicted value of the satellite attitude error angular velocity, a one-step predicted value of the reaction flywheel angular momentum, a one-step predicted value of the reaction flywheel friction moment, a one-step predicted value of the external disturbance moment and a one-step predicted value of the fiber-optic gyroscope constant drift by using a derivative of the satellite attitude error quaternion, a derivative of the satellite attitude error angular velocity, a derivative of the reaction flywheel angular momentum, a derivative of the flywheel friction moment, a derivative of the external disturbance moment and a fiber-optic gyroscope constant drift derivative in the linear integration step two;
step four, performing deviation calculation on the one-step predicted values of the satellite attitude error quaternion, the satellite attitude error angular velocity, the angular momentum of the reaction flywheel, the friction moment of the reaction flywheel, the external interference moment and the fiber-optic gyroscope constant drift obtained in the step three at the current moment, the satellite attitude error angular velocity and the angular momentum of the reaction flywheel obtained in the step one, and the previous-moment estimated value of the reaction flywheel friction moment, the external interference moment estimated value and the fiber-optic gyroscope constant drift estimated value recorded in the step one to respectively obtain deviation amounts with the one-step predicted information values;
recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment by utilizing the first step, and obtaining a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the current moment by linear weighting of the deviation amount of the one-step prediction information value obtained in the fourth step;
sixthly, amplitude limiting judgment and operation are carried out on the quaternion estimation value of the satellite attitude error at the current moment, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of a reaction flywheel, the friction moment estimation value of the reaction flywheel, the external disturbance moment estimation value and the constant drift estimation value of the fiber-optic gyroscope, and the accurate quaternion estimation value of the satellite attitude error, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of the reaction flywheel, the friction moment estimation value of the reaction flywheel, the external disturbance moment estimation value and the constant drift estimation value of the fiber-optic gyroscope at the current moment are obtained;
and seventhly, at the next moment, taking the satellite attitude error quaternion estimated value, the satellite attitude error angular velocity estimated value, the reaction flywheel angular momentum estimated value, the reaction flywheel friction torque estimated value, the external disturbance torque estimated value and the fiber-optic gyroscope constant drift estimated value which are obtained in the sixth step and are accurate at the current moment as the satellite attitude error quaternion estimated value, the attitude error angular velocity estimated value, the reaction flywheel angular momentum estimated value, the reaction flywheel friction torque estimated value, the external disturbance torque estimated value and the fiber-optic gyroscope constant drift estimated value at the previous moment in the first step, and repeatedly executing the first step to realize the combined accurate estimation of the attitude control information.
The invention has the beneficial effects that: the method comprehensively considers the joint estimation problems of six variables of the attitude error quaternion, the attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment and the fiber-optic gyroscope constant drift, realizes the determination of the high-precision satellite attitude control information in a circular iteration mode, and is used for satellite attitude control. The method starts from the algorithm of software to improve the determination precision of the attitude information under the condition of not increasing the hardware configuration of the satellite-borne sensor or the executing mechanism, is simple and easy to implement and is convenient to realize on track.
Drawings
FIG. 1 is a flow chart of an attitude control information joint estimation algorithm under small angle deviation of attitude;
FIG. 2 is a diagram showing the Euler angle comparison (321 in turn) effect of rolling axis trueness and estimation error during satellite attitude maneuver;
FIG. 3 is a diagram showing Euler angle comparison (321 in sequence) effects of true and estimated errors of a pitch axis during a satellite attitude maneuver;
FIG. 4 is a graph showing Euler angle comparison (321 rotation order) effects of yaw axis trueness and estimation error during satellite attitude maneuver;
FIG. 5 is a diagram showing the comparison effect between the true rolling axis and the estimated error angular velocity in the satellite attitude maneuver process;
FIG. 6 is a diagram showing the comparison between the true pitch axis and the estimated error angular velocity during the satellite attitude maneuver;
FIG. 7 is a diagram illustrating the effect of comparing the true yaw axis and the estimated error angular velocity during the satellite attitude maneuver;
FIG. 8 is a diagram showing the comparison effect of the rolling axis reality and the estimated flywheel angular momentum during the satellite attitude maneuver;
FIG. 9 is a diagram showing the comparison effect of the true pitch axis and the estimated flywheel angular momentum during the satellite attitude maneuver;
FIG. 10 is a diagram illustrating the comparison effect of the true yaw axis and the estimated flywheel angular momentum during the satellite attitude maneuver;
FIG. 11 is a diagram showing the comparison effect of the rolling axis trueness and the estimated flywheel friction torque during the satellite attitude maneuver;
FIG. 12 is a graph showing the comparison between the true pitch axis and the estimated flywheel friction torque during satellite attitude maneuver;
FIG. 13 is a diagram showing the comparison effect of the actual yaw axis and the estimated flywheel friction torque during the satellite attitude maneuver;
FIG. 14 is a diagram showing the comparison effect of true rolling axis and estimated gyro drift during satellite attitude maneuver;
FIG. 15 is a graph of pitch axis trueness and estimated gyro drift contrast effect during satellite attitude maneuver;
FIG. 16 is a graph of yaw axis trueness and estimated gyro drift contrast effect during satellite attitude maneuver;
FIG. 17 is a diagram showing the comparison effect of the true rolling axis and the estimated spatial disturbance moment during the satellite attitude maneuver;
FIG. 18 is a diagram showing the comparison effect of the true pitch axis and the estimated spatial disturbance moment during the satellite attitude maneuver;
FIG. 19 is a diagram showing the comparison effect of the real yaw axis and the estimated spatial disturbance moment during the satellite attitude maneuver.
Detailed Description
In the first embodiment, the first embodiment is described with reference to fig. 1 to 19, and the attitude control information joint estimation method under the satellite attitude angle deviation is based on the measurement information of the satellite-borne sensor and the actuator, and uses a satellite attitude dynamics, kinematics and a reaction flywheel dynamics model to realize the joint accurate estimation of six variables, namely, an attitude error quaternion, an attitude error angular velocity, a reaction flywheel angular momentum, a reaction flywheel friction moment, an external disturbance moment and a fiber-optic gyroscope constant drift through iterative computation, so as to provide accurate input for an attitude control algorithm. Specifically, the method comprises the following steps:
step A, respectively acquiring current measurement values of a star sensor, a fiber-optic gyroscope, a reaction flywheel and a GPS through a satellite-borne central machine to obtain a satellite attitude measurement quaternion q at the current momentcSatellite attitude measurement angular velocity wcAngular momentum H of reaction flywheelcWith GPS time tcAnd so on.
Step B, quaternion q according to given expected attitudehAnd desired attitude angular velocity whBy measuring quaternion q with the satellite attitude at the current timecSatellite attitude measurement angular velocity wcPerforming deviation calculation to obtain the quaternion q of the satellite attitude error at the current momenteAnd attitude error angular velocity we. And meanwhile, recording estimated values Xest (t-1) of six variables, namely a satellite attitude error quaternion, an attitude error angular velocity, a reaction flywheel angular momentum, a reaction flywheel friction moment, an external disturbance moment and a fiber-optic gyroscope constant drift at the previous moment.
And C, calculating the derivative of the attitude error quaternion, the derivative of the attitude error angular velocity and the derivative of the reaction flywheel angular momentum according to the satellite attitude dynamics and kinematics equation and the reaction flywheel dynamics model based on the estimated values Xest (t-1) of the satellite attitude error quaternion, the attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment, the fiber-optic gyroscope constant value offset and the like at the previous moment recorded in the step B. And setting the derivative of the friction moment of the reaction flywheel to be zero, the derivative of the external disturbance moment to be zero and the derivative of the constant drift of the fiber-optic gyroscope to be zero.
The satellite attitude dynamics and kinematics equation is as follows:
here, the control coordinate axis of the satellite is basically the main axis, and the rotational inertia matrix of the satellite is taken as I ═ diag (I)x,Iy,Iz). Definition x ═ wxwywzq0q1q2q3]TIs the state vector of the system, u ═ TxTyTz]TFor counteracting the control moment input vector of the flywheel, d ═ TdxTdyTdz]TAnd inputting a vector for the space disturbance moment of the system.
The kinetic equation for the reaction flywheel is as follows:
here, the first and second liquid crystal display panels are,
the derivative of the flywheel angular momentum is u (t), the control moment input vector at the moment t of the reaction flywheel is u (t-1), and the control moment input vector at the moment t-1 of the reaction flywheel is u (t-1).
And D, taking the estimation values Xest (t-1) of the satellite attitude error quaternion, the attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment, the fiber-optic gyroscope constant value offset and the like at the previous moment recorded in the step B as initial values, taking a preset control period as integration duration, and obtaining one-step prediction values Xpredictive (t) of the six variables of the satellite attitude error quaternion, the satellite attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment and the fiber-optic gyroscope constant value drift at the current moment through the derivative of each variable in the linear integration step C.
Step E, utilizing the satellite attitude error quaternion at the current moment, the satellite attitude error angular velocity, the angular momentum of the reaction flywheel, the friction moment of the reaction flywheel, the external disturbance moment and the one-step predicted value Xpredictive (t) of the fiber-optic gyroscope constant drift, and the satellite attitude error quaternion q at the current moment obtained in the step BeAngular velocity w of attitude erroreAnd reaction flywheel angular momentum HcAnd recording the information of the friction torque estimated value of the reaction flywheel, the external disturbance torque estimated value, the constant drift estimated value of the fiber-optic gyroscope and the like at the previous moment in the step BAnd calculating deviation to obtain the deviation amount Xerror from the one-step prediction information value.
And F, obtaining the estimated values Xest (t) of six variables, namely the quaternion of the satellite attitude error, the angular velocity of the attitude error, the angular momentum of a reaction flywheel, the friction moment of the reaction flywheel, the external disturbance moment and the constant shift of the fiber-optic gyroscope at the current moment, which are recorded in the step B, by linear weighting of the estimated values of the quaternion of the satellite attitude error, the angular momentum of the reaction flywheel, the external disturbance moment, the constant shift of the fiber-optic gyroscope and the like at the previous moment and the deviation quantity of the one-step predicted information value (the weighting coefficient is a parameter to be adjusted). The specific formula is as follows:
Xest(t)＝Xest(t-1)+K×Xerror
wherein K is an adjustable weighting parameter.
And G, carrying out amplitude limiting judgment and operation on estimated values Xest (t) of the satellite attitude error quaternion, the satellite attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment, the fiber-optic gyroscope constant value offset and the like at the current moment, and further obtaining estimated values Xuse (t) of six variables of the satellite attitude error quaternion, the satellite attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment and the fiber-optic gyroscope constant value drift which are accurate at the current moment.
And step H, at the next moment, taking the estimated values Xuse (t) of six variables, namely the accurate satellite attitude error quaternion at the current moment, the satellite attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment and the fiber-optic gyroscope constant drift, obtained in the step G as the estimated values Xest (t-1) of the satellite attitude error quaternion, the attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment, the fiber-optic gyroscope constant drift and the like at the previous moment recorded in the step B, and repeatedly performing the step A to realize the combined accurate estimation of attitude control information and the like.
In this embodiment, a microsatellite of a certain type is taken as an example, and the moment of inertia matrix is assumed as follows:
here, it is considered that the satellite attitude is maneuvered and stabilized from the three-axis-to-sun mode to the three-axis-to-ground mode. The effect of the estimation method proposed by the present invention is shown in fig. 2-19. And when the simulation time is 115.4s, the attitude deviation enters a small-angle set value range, and an estimation algorithm is started to estimate the attitude error quaternion, the attitude error angular velocity, the reaction flywheel angular momentum, the reaction flywheel friction moment, the external disturbance moment and the fiber-optic gyroscope constant drift.
Claims (2)
1. The attitude control information joint estimation method under the satellite attitude angle deviation is characterized by comprising the following steps of:
respectively acquiring current measurement values of a star sensor, a fiber-optic gyroscope, a reaction flywheel and a GPS through a satellite-borne central machine to obtain a satellite attitude measurement quaternion, a satellite attitude measurement angular velocity, an angular momentum of the reaction flywheel and GPS time information at the current moment, and performing deviation calculation on a given expected attitude quaternion and an expected attitude angular velocity with the satellite attitude measurement quaternion and the satellite attitude measurement angular velocity at the current moment to obtain a satellite attitude error quaternion and a satellite attitude error angular velocity at the current moment; simultaneously, recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment;
recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment based on the step one, and respectively calculating a satellite attitude error quaternion derivative, a satellite attitude error angular velocity derivative and a reaction flywheel angular momentum derivative according to a satellite attitude dynamics and kinematics equation and a reaction flywheel dynamics model; setting the derivative of the friction moment of the reaction flywheel as zero, the derivative of the external disturbance moment as zero, and the derivative of the constant drift of the fiber-optic gyroscope as zero;
taking the quaternion estimation value of the satellite attitude error, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of a reaction flywheel, the friction torque estimation value of the reaction flywheel, the external disturbance torque estimation value and the constant offset estimation value of the fiber-optic gyroscope recorded in the step one as initial values;
taking a preset control period as an integral duration, and obtaining a one-step predicted value of the satellite attitude error quaternion, a one-step predicted value of the satellite attitude error angular velocity, a one-step predicted value of the reaction flywheel angular momentum, a one-step predicted value of the reaction flywheel friction torque, a one-step predicted value of the external disturbance torque and a one-step predicted value of the fiber-optic gyroscope constant drift at the current moment through a derivative of the satellite attitude error quaternion, a derivative of the satellite attitude error angular velocity, a derivative of the reaction flywheel angular momentum, a derivative of the external disturbance torque and a fiber-optic gyroscope constant drift derivative in the linear integration step two;
step four, performing deviation calculation on the one-step predicted values of the satellite attitude error quaternion, the satellite attitude error angular velocity, the angular momentum of the reaction flywheel, the friction moment of the reaction flywheel, the external interference moment and the fiber-optic gyroscope constant drift obtained in the step three at the current moment, the satellite attitude error angular velocity and the angular momentum of the reaction flywheel obtained in the step one, and the previous-moment estimated value of the reaction flywheel friction moment, the external interference moment estimated value and the fiber-optic gyroscope constant drift estimated value recorded in the step one to respectively obtain deviation amounts from the one-step predicted values;
recording a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the previous moment by utilizing the first step, and carrying out linear weighting on the deviation amount of the predicted value obtained in the fourth step to obtain a satellite attitude error quaternion estimated value, a satellite attitude error angular velocity estimated value, a reaction flywheel angular momentum estimated value, a reaction flywheel friction torque estimated value, an external disturbance torque estimated value and a fiber-optic gyroscope constant drift estimated value at the current moment;
sixthly, amplitude limiting judgment and operation are carried out on the quaternion estimation value of the satellite attitude error at the current moment, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of a reaction flywheel, the friction moment estimation value of the reaction flywheel, the external disturbance moment estimation value and the constant drift estimation value of the fiber-optic gyroscope, and the accurate quaternion estimation value of the satellite attitude error, the angular velocity estimation value of the satellite attitude error, the angular momentum estimation value of the reaction flywheel, the friction moment estimation value of the reaction flywheel, the external disturbance moment estimation value and the constant drift estimation value of the fiber-optic gyroscope at the current moment are obtained;
and seventhly, at the next moment, taking the satellite attitude error quaternion estimated value, the satellite attitude error angular velocity estimated value, the reaction flywheel angular momentum estimated value, the reaction flywheel friction torque estimated value, the external disturbance torque estimated value and the fiber-optic gyroscope constant drift estimated value which are obtained in the sixth step and are accurate at the current moment as the satellite attitude error quaternion estimated value, the attitude error angular velocity estimated value, the reaction flywheel angular momentum estimated value, the reaction flywheel friction torque estimated value, the external disturbance torque estimated value and the fiber-optic gyroscope constant drift estimated value at the previous moment in the first step, and returning to the first step to realize the combined accurate estimation of the attitude control information.
2. The method according to claim 1, wherein in step three, the one-step predicted value of the quaternion of the satellite attitude error at the current time, the one-step predicted value of the angular velocity of the satellite attitude error, the one-step predicted value of the angular momentum of the reaction flywheel, the one-step predicted value of the friction torque of the reaction flywheel, the one-step predicted value of the external disturbance torque, and the one-step predicted value of the constant drift of the fiber-optic gyroscope are obtained by one-step linear integral calculation.
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| CN108313330B (en) * | 2018-03-28 | 2021-10-01 | 上海航天控制技术研究所 | Satellite interference torque estimation method based on augmented Kalman filtering |
| CN108839824B (en) * | 2018-05-16 | 2021-09-24 | 南京航空航天大学 | Hybrid actuator momentum optimization management method based on cooperative game |
| CN109141471B (en) * | 2018-06-28 | 2020-07-10 | 上海卫星工程研究所 | Implementation method for screening high-stability satellite flywheel based on micro-interference torque |
| CN109634294B (en) * | 2018-12-10 | 2022-01-04 | 上海航天控制技术研究所 | Anti-interference quaternion attitude maneuver path planning method based on maneuver capability identification |
| CN110329548B (en) * | 2019-05-24 | 2023-01-17 | 中国人民解放军63789部队 | Flywheel system reconstruction method under on-orbit rotation bias control of spacecraft |
| CN110389592B (en) * | 2019-07-18 | 2020-12-01 | 南京航空航天大学 | Spacecraft attitude control method based on distributed intelligent flywheel |
| CN111319792A (en) * | 2020-02-18 | 2020-06-23 | 北京空间飞行器总体设计部 | GEO satellite interference torque acquisition method based on-orbit telemetry data |
| CN111532453B (en) * | 2020-05-11 | 2023-04-25 | 鲁东大学 | Fixed-time anti-interference attitude control method for rigid body micro-nano satellite |
| CN112572835B (en) * | 2020-12-15 | 2022-07-05 | 长光卫星技术股份有限公司 | Satellite in-orbit angular momentum management and control method with attitude switching function |
| CN113686334B (en) * | 2021-07-07 | 2023-08-04 | 上海航天控制技术研究所 | Method for improving on-orbit combined filtering precision of star sensor and gyroscope |
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| CN100356139C (en) * | 2005-01-21 | 2007-12-19 | 清华大学 | Miniature assembled gesture measuring system for mini-satellite |
| CN101696884B (en) * | 2009-11-05 | 2012-08-08 | 中国人民解放军国防科学技术大学 | Method for determining spatial attitude accuracy of satellite |
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